# Questions tagged [taylor-expansion]

Questions regarding the Taylor series expansion of univariate and multivariate functions, including coefficients and bounds on remainders. A special case is also known as the Maclaurin series.

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### How to decide if a DE has a singular point at infinity, and if so, what to do about it.

I'm trying to understand singular points at infinity, so looking at the example $$x^2(1-x^2)y'' - y = 0$$ I am trying to investigate (a) does it have a singular point at infinity, and (b) if it ...
3answers
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### show that $|\sin(1)-0.841|\leq10^{-3}$

My textbook states that $|\sin(1)-0.841|\leq10^{-3}$ but I do not know how this could be true. It also gives a table showing values of ${1\over n!}\pm10^{-8}$ when $n$ is $1$ to $10$. The reason why ...
2answers
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### How to get the result of only first N terms of a geometric series like $1+Ax+Ax^2+Ax^3+Ax^4+Ax^5$… [duplicate]

Given -1 < x < 1, and for Series like the following, I am trying to figure out not the complete Total, but only the Total of first N Terms. So the Question is: What is the Total of first N ...
3answers
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### What is $1+Ax+Ax^2+Ax^3+Ax^4+Ax^5$… an expansion of ?? [closed]

$$1 + x+ x^2 + x^3 + x^4+ x^5 + x^6...$$ is the expansion of $\frac{1}{1-x},$ and $$1 - x + x^2 - x^3 + x^4 - x^5 + x^6...$$ is the expansion of $\frac{1}{1+x}.$ I am trying to figure out of what ...
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### First Order Approximation of a $\sqrt{3.9}$

Use the first order approximation to determine $\sqrt{3.9}$. Use your calculator to determine the error in your approximation. I am really confused by this question. There is no function so I don't ...
1answer
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